We present a parameter study of the magnetohydrodynamical dynamo driven by
cosmic rays in the interstellar medium (ISM) focusing on the efficiency of
magnetic field amplification and the issue of energy equipartition between
magnetic, kinetic and cosmic ray (CR) energies. We perform numerical CR-MHD
simulations of the ISM using the extended version of ZEUS-3D code in the
shearing box approximation and taking into account the presence of Ohmic
resistivity, tidal forces and vertical disk gravity. CRs are supplied in
randomly distributed supernova (SN) remnants and are described by the
diffusion-advection equation, which incorporates an anisotropic diffusion
tensor. The azimuthal magnetic flux and total magnetic energy are amplified
depending on a particular choice of model parameters. We find that the most
favorable conditions for magnetic field amplification correspond to magnetic
diffusivity of the order of 3\times 10^{25} \cm^2\s^{-1}, SN rates close to
those observed in the Milky Way, periodic SN activity corresponding to spiral
arms, and highly anisotropic and field-aligned CR diffusion. The rate of
magnetic field amplification is relatively insensitive to the magnitude of SN
rates in a rage of spanning 10% up to 100% of realistic values. The timescale
of magnetic field amplification in the most favorable conditions is 150 Myr, at
galactocentric radius equal to 5 kpc. The final magnetic field energies
fluctuate near equipartition with the gas kinetic energy. In all models CR
energy exceeds the equipartition values by a least an order of magnitude, in
contrary to the expected equipartition. We suggest that the excess of cosmic
rays can be attributed to the fact that the shearing-box does not permit cosmic
rays to leave the system along the horizontal magnetic field.Comment: 12 papges, 11 figures, accepted for publication in Astronomy and
Astrophysic